1991 AJHSME Problems/Problem 14
Contents
Problem
Several students are competing in a series of three races. A student earns points for winning a race, points for finishing second and point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student?
Solution
There are two ways for a student to get : and . Clearly if someone gets one of these combinations someone else could get the other, so we are not guaranteed the most points with .
There is only one way to get points: . In this case, the largest score another person could get is , so having points guarantees having more points than any other person .
Solution 2
If someone gets points, the possible combinations are and If he gets then someone else can be which would not guarantee victory. If we have 13 points, the only way to make this is . There is no way to get any number of points higher than this, so the answer is .---stjwyl
See Also
1991 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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